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Finding the Third Proportional to 729 and 1,971

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Solution

The third proportional to 729 and 1,971 is: 5,329

Step by Step Solution

  1. Step 1: Write the proportion equation
    729 : 1,971 = 1,971 : x
  2. Step 2: Convert to fraction form
    729/1,971 = 1,971/x
  3. Step 3: Cross multiply
    729x = 1,971 × 1,971
  4. Step 4: Simplify right side
    729x = 3,884,841
  5. Step 5: Solve for x
    x = 3,884,841/729
  6. Step 6: Final answer
    x = 5,329

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Why These Related Problems?

These problems maintain the same ratio (2.70) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.